Solve a*a*a*a+a

$$a \cdot a \cdot a \cdot a + a$$

Evaluate

$$a^{4}+a$$

Solution Steps

Multiply a and a to get a^{2}.

$$a^{2}aa+a$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$a^{3}a+a$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$a^{4}+a$$

Factor

$$a\left(a+1\right)\left(a^{2}-a+1\right)$$

Solution Steps

Factor out a.

$$a\left(aaa+1\right)$$

Consider a^{3}+1. Rewrite a^{3}+1 as a^{3}+1^{3}. The sum of cubes can be factored using the rule: p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right).

$$\left(a+1\right)\left(a^{2}-a+1\right)$$

Rewrite the complete factored expression. Polynomial a^{2}-a+1 is not factored since it does not have any rational roots.

$$a\left(a+1\right)\left(a^{2}-a+1\right)$$